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PEIRCE-L Digest 1325 - March 12, 1998
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From PEIRCE-L Forum, Jan 5, 1998, [name of author of message],
"re: Peirce on Teleology"
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sue include:
1) Re: Logic Naturalized : Truth
by a.freadman[…]mailbox.uq.edu.au (A. Freadman)
2) Re: Logic Naturalized : Truth
by Tom Burke
3) Re: Logic Naturalized : Truth
by joseph.ransdell[…]yahoo.com (ransdell, joseph m.)
4) Re: Tears From Heaven
by patcop[…]bo.nettuno.it (Patrick J. Coppock)
5) Re: Logic Naturalized : Truth
by Howard Callaway
6) Re: Logic Naturalized : Truth
by Hugo Fjelsted Alroe
7) Dyadic vs. Triadic?
by Howard Callaway
8) RE: Logic Naturalized : Truth
by Cathy Legg
9) Re: Logic Naturalized?
by Cathy Legg
10) Re: Logic Naturalized : Truth
by Howard Callaway
----------------------------------------------------------------------
Date: Thu, 12 Mar 1998 06:03:31 +1100
From: a.freadman[…]mailbox.uq.edu.au (A. Freadman)
To: peirce-l[…]ttacs6.ttu.edu
Subject: Re: Logic Naturalized : Truth
Message-ID: <199803112003.GAA09761[…]yowie.cc.uq.edu.au>
I agree with you, Joe: I don't think the syntax/semantics distinction can
be accommodated byPeirce, either, and I've always supposed that Morris'
reading of Peirce in respect of what became the standard - and unexamined -
distinction of semiotics (syntax/semantics/pragmatics) was a serious
distortion on a number of counts. But it has become difficult to dislodge
- the whole disciplinary organisation of linguistics presupposes it.
Anne
------------------------------
Date: Wed, 11 Mar 1998 15:09:46 -0500
From: Tom Burke
To: peirce-l[…]ttacs6.ttu.edu
Subject: Re: Logic Naturalized : Truth
Message-ID:
At 7:28 AM -0500 3/11/98, Joseph Ransdell wrote:
>Tom Burke says:
>> I'm all in
>>favor of Peirce's broader conception of logic, and it can all be preserved
>>for all I know. But there's nothing to say this broader conception cannot
>>be filled out a bit and otherwise informed by contemporary developments.
>
>In contrast to the view I supposedly hold, that it can't be filled out or
>otherwise informed by contemporary developments? I don't recall saying
>anything to that effect.
No no no. I wasn't claiming this at all. I was trying to explain what *I*
was saying in suggesting that the syntax/semantics distinction is something
Peirce might have profitably considered. Namely, it's not a matter of
identifying s/s as two of the three branches of logic, but rather of using
the s/s distinction to fill out details of each of the three branches.
----
>I do recall saying something to the effect that I
>do not see how his view can accommodate the syntax-semantics distinction
>unless the people who draw that distinction are not assuming the dyadic
>conception of a sign, as was assumed in the Carnap-Morris tradition that
>was restated in hundreds of logic texts for several decades thereafter.
This is the only thing in what you said that I took issue with -- namely,
that employing the s/s distinction might limit us to some kind of dyadic
view of logic. Such a view is a definite no-no for Peircean logic. But
surely a dyadic conception is not the only way to think about the s/s
distinction.
----
>You seem to be claiming that their conception was somehow left behind in
>the contemporary understanding of the distinction. I don't dispute that,
>though I was previously unaware of it but I am raising the question of what
>the contemporary conception is that makes it importantly different from
>that of Carnap and Morris.
I certainly have no desire to revitalize the Carnap/Morris view of syntax
and semantics. That is just one view. We can put that view aside, but
still inquire into the possible value of the distinction in some form or
other -- perhaps an entirely new conception unheard of up to now so far as
that goes. Unfortunately I have no specific suggestions to make here; but
I am simply puzzled about what connections might be made and how it might
be done.
The contemporary (post-1980) view of logical syntax and semantics that I
have in mind is best represented, I think, by the elementary textbooks
"Hyperproof" and "The Language of First-Order Logic" by Barwise and
Etchemendy -- especially "Hyperproof". They make a clear and convincing
and easily understood distinction there (post-Carnap) between consequence
relations and provability relations. And I'm quite baffled about how to
map this onto Peirce's view of logic.
E.g., when Peirce describes "Critic" as the branch of logic which
"classifies arguments and determines the validity and degree of force of
each kind" -- this no doubt includes deductive, inductive, and abductive
argument forms. With regard to deductive argument forms in particular,
there is a question here of whether he is talking about arguments as
consequence relations or as provability relations (in the
Barwise/Etchemendy sense). So far as I can tell, Peirce did not clearly
draw any such distinction, so it's up in the air as to how to answer the
question. He didn't assert that the distinction between consequence and
provability was invalid, but rather he simply did not consider the
distinction clearly enough to render such a judgment one way or the other.
By default, I would be inclined to think that Peirce was basically a
semanticist (in all three branches of logic); though like Russell his work
perhaps suffered from not distinguishing clearly enough semantic form and
syntactic form. In CP4:358, Peirce writes:
CP4:358. The view which pragmatic logic takes of the predicate, in
consequence of its assuming that the entire purpose of deductive logic is
to ascertain the necessary conditions of the truth of signs, without any
regard to the accidents of Indo-European grammar, will be here briefly
stated.
>From this it seems to me that Peirce is primarily interested in semantics,
not simply grammar (syntax?). And what he is calling a "predicate" is what
in contemporary parlance would be called a property-or-relation. I.e.,
first-order grammars utilize predicate symbols, among other things; and
these predicate symbols express (stand for, mean) first-order properties or
relations. E.g., the ">Goedel's incompleteness results establish that syntax and semantics (in a
>>contemporary sense of these terms) are not the same thing.
>
>Does Goedel himself use the syntax/semantics distinction? I mean
>explicitly? Or is this rather the usual way of reconstructing his view by
>contemporary formalists? That could be very important. I once wasted many
>months reconstructing Alan Turing's conceptions in his 1936-37 paper on
>number in such a way as to show that there was no need for him to assume
>the syntax-semantics distinction, only to discover that there was no need
>for me to disentangle it from his thought since Turing himself made no use
>of it to begin with, my mistake being to trust the standard accounts of
>what he does in that paper -- the paper from which the "Turing machine"
>conception arises -- by the logicians, chiefly Kleene's, which has been the
>most influential.
This is why I mentioned Tarski in my earlier post. It was really Tarski's
semantic conception of satisfaction and truth for first-order languages
which "clarified" the semantics/syntax distinction, whereas Goedel, Turing,
and others at the time were for all intents and purposes syntacticists. (I
now see perhaps what Cathy was getting at.) Carnap unsuccessfully tried to
formalize this distinction one way, but Tarski's "successful" way of doing
it became the standard. Kleene and others were not just trying to give
watered-down accounts (reconstructions?) of what Turing and Goedel did, but
to reconcile (reconstruct?) what they (Turing, Goedel) did and/with a
Tarskian conception of semantics. Whether it was Goedel himself personally
or the overall community of logicians at the time who "established" (i.e.,
settled on the belief) that syntax and semantics are not the same thing is
really not the issue. But that's what Goedel's results eventually come
down to. (Similarly, what we often refer to as Newtonian physics is not
exactly what Newton himself did, but is the result of many inquirers
working out the details but otherwise appropriately calling the results
"Newtonian".)
The thing about Tarskian semantics is that it employs not much more than
simple set theory to specify domains of quantification, etc etc. Peircean
semantics turns on his far more complicated triadic category system, with
all sorts of interesting recursions and convolutions and diagrammatic
constructions which ... well, simply make me dizzy. The one positive
thesis that I am trying to formulate here, so far as I understand any of it
at all, is that when Peirce talks about deduction, the best way to read him
from a contemporary perspective is that he is referring to formal semantic
consequence rather than syntactic provability as such. I should rather
call this a question rather than a thesis. Would it be helpful if we think
of Peircean logic (semiotics, sign theory, or what?) primarily as an
alternative to set theory as the basic means by which semantic domains are
specified?
----
>> So far as I can
>>tell, Peirce never even considered the question. Is this because it is
>>irrelevant or fallacious? Or did Peirce perhaps not have the last word on
>>what logic is all about -- as if there might be some important and even
>>basic things that he missed?
>
>My view being, of course, that he did have the last word on logic and there
>could be nothing important or basic that he missed.
I can't really say what your view is, and I was not singling you out when I
wrote the above; but these are questions we all should gladly ask, I would
think.
----
>> The latter possibility ought to be seriously
>>considered in the process of reconciling Peircean logic with contemporary
>>logic. Peirce scholarship has nothing to lose and everything to gain no
>>matter how that turns out.
>
>I could probably be persuaded from my dogmatism, but I don't think the main
>point I was trying to make has been considered in what you say, namely,
>that Peirce cannot be brought "up to date" if that means interjecting into
>his theory the conception of a sign which was at one time, at least, a part
>of the basis for the distinction in question.
I guess I missed your point, and am probably still missing it. But my
point is not to bring Peirce "up to date" but rather to suggest that we try
to reconcile Peircean logic with contemporary logic as much as possible --
and if that means undermining contemporary logic, then so be it. Ditto for
Peircean logic. As it stands, Peircean logicians and contemporary
logicians are simply talking past each other, as if working "dogmatically"
(as you say) in totally different universes. Instead, each could be taken
as a measure of the other; and the eventual result might be some kind of
hybrid conception of logic which vindicates all concerned. But we can't
dismiss contemporary logic straightaway just because Morris and Carnap got
it wrong. I would prefer to take Barwise and Etchemendy as representatives
of contemporary logic and otherwise hope that addressing these questions
could look to the present and future (where Peirce is still waiting or us)
rather than dwell on old debates.
Thanks for your responses, Joe.
--TB
______________________________________________________________________
Tom Burke http://www.cla.sc.edu/phil/faculty/burket
Department of Philosophy Phone: 803-777-3733
University of South Carolina Fax: 803-777-9178
For a list of common LISTSERV User Commands see
http://www.cla.sc.edu/phil/faculty/burket/listserv.html
------------------------------
Date: Wed, 11 Mar 1998 17:34:30 -0600
From: joseph.ransdell[…]yahoo.com (ransdell, joseph m.)
To:
Subject: Re: Logic Naturalized : Truth
Message-ID: <001601bd4d46$3e3d5be0$90e6ead0[…]ransdell.door.net>
Tom Burke says:
>The contemporary (post-1980) view of logical syntax and semantics that
I
>have in mind is best represented, I think, by the elementary textbooks
>"Hyperproof" and "The Language of First-Order Logic" by Barwise and
>Etchemendy -- especially "Hyperproof". They make a clear and
convincing
>and easily understood distinction there (post-Carnap) between
consequence
>relations and provability relations. And I'm quite baffled about how
to
>map this onto Peirce's view of logic.
This connection seems promising to me prima facie, given the similarity
of their idea of observational proof based on pictorial representation
with Peirce's idea of theoremetic reasoning in mathematics. I haven't
read or worked with the "Hyperproof" text but the description of the
conception of proof they give elsewhere often sounds like it IS Peirce
when he talks about theorematic deduction. I'll have to read more on
this, though, before I can say anything in a substantive way on this.
> The one positive
>thesis that I am trying to formulate here, so far as I understand any
of it
>at all, is that when Peirce talks about deduction, the best way to read
him
>from a contemporary perspective is that he is referring to formal
semantic
>consequence rather than syntactic provability as such. I should rather
>call this a question rather than a thesis. Would it be helpful if we
think
>of Peircean logic (semiotics, sign theory, or what?) primarily as an
>alternative to set theory as the basic means by which semantic domains
are
>specified?
My guess is that the idea of syntactic provability would seem to him
almost a contradiction in terms since it seems to imply a severance of
the conception of proof from the conception of truth, whereas he regards
critical logic as a sort of explication of the latter. As regards set
theory, I am inclined to say that, yes, his logic should probably be
regarded as if intended to be an alternative to that. Isn't the
set-theoretic approach essentially connected with the idea that number
is to be understood in such a way that cardinal number is in some sense
prior to ordinal number? I should think that Peirce would be committed
to the contrary view. But I am not talking from a position of
confidence on any of this but only projecting intuitively from
tendencies I already know to be in Peirce's thinking.
Best regards,
Joe R.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Joseph Ransdell or <>
Department of Philosophy, Texas Tech University, Lubbock TX 79409
Area Code 806: 742-3158 office 797-2592 home 742-0730 fax
ARISBE: Peirce Telecommunity website - http://members.door.net/arisbe
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
:
------------------------------
Date: Thu, 12 Mar 1998 10:09:55 +0100 (MET)
From: patcop[…]bo.nettuno.it (Patrick J. Coppock)
To: peirce-l[…]ttacs6.ttu.edu
Subject: Re: Tears From Heaven
Message-ID:
Hello again Anne. Nice to hear from you. You wrote:
--Anne--------------
This says that "words", and maps, are "embodied", and "subjective" in this
sense, that they cannot divest themselves of their "position of enunciation
(or observation, or whatever); then the question about the law of gravity
has to be restated: the position represented by "Sokal" would have it that
the law of gravity is not a representation; your response (I know that it
is a joke) says that it is. But Peirce I am sure would want to argue that
the opposition between these two positions is false. Things like the law
of gravity are the outcome of a whole range of representational
practices,which mediate, or articulate, each other's relativity. I guess
it's true to say that Einstein's contribution is to say exactly in so far
as what the outcome of these representations is governed by the point of
observation, and what difference it makes to know so.
--end----------------
Yes, since Peirce was a believer (as I am too) in the scientific method, I
think a key word (or rather phrase) here is what you refer to above as
"representational practices". I wonder if we mean the same thing with this
term?
The historical process of the discovery and formulation of the law of
gravity as we now understand it most certainly have involved very many
different kinds of representational practices over time. To begin with
there are those kinds of practices which are motivated by our personal (or
"private") experience (we are all probably able to understand for instance
after falling out of bed and thinking about that a bit, that we would not
either be able to walk upside down on the dining room ceiling without a lot
of special equipment, and even then with great difficulty), observations of
what happens most of the time to other people and objects due to the
effects of gravity (and when it doesn't we of course start to wonder why),
as well as the various kinds of cognitive and other (talking about and
sharing experiences, observations and ideas, scribbling notes on scraps of
paper, drawing diagrams, devising experiments and measuring instruments
etc.) practices involved on the part of those thinkers and doers who
actually took part in formulating the law in its present representations in
mathematical, linguistic or other kinds of terms.
What I guess I was trying to draw attention to (apart of course from
wishing Mark good luck with his eye op.) in my posting (and don't ask me
exactly why I was trying to do so yet, because I am not really quite sure)
was the need to account for what we could call the "experiential" - which
is what I perhaps should have used instead of using "subjective" - side of
such representational practices, seen within the wider process of the
discovery and formulation of scientific meanings in the form of "laws".
"The experiential side of such representational practices" here being used
in the sense of what I referred to in my posting to Mark as "embodied"
experience (and I guess that means intentionally or otherwise motivated
experience), and which again is another way of saying that the basic
experience we have of being a human being in a flesh, blood and whatever
else it may be (fat, hormone patches, contact lenses, hearing aids,
implants, pacemakers etc. etc.), body constitutes in itself (*per se*) a
rather special kind of, as you put it, "position of enunciation (or
observation, or whatever)". Now just how important this embodied experience
actually is in the larger picture of things I am not quite sure, but it
most certainly plays a very central role in how we mortals understand the
world. Horst Ruthrof has some interesting discussions of this, also with
reference to Peirce in his recent book "Semantics and the body: Meaning
from Frege to the postmodern", Univerity of Toronto Press, 1997, where he
amongst other things cites and interprets Peirce as follows:
"Climbing down the transcendental ladder towards the base conditions of
signs, Peirce suggests that all significatory processes are ultimately
grounded 'either in an idea predominantly of feeling or in one
predominantly of acting and being acted on.' At this base line semiosis
arises 'from the experience of volition and the experience of the
perception of phenomena' - in other words, from the body" (p. 29)
The relevant section in the CP is apparently 5.7 (I don't have them here on
hand in order to check exactly what is Peirce and what is Ruthrof here,
maybe someone else can?)
In any case, to return to our present discussion of the role of
representational practices in the discovery and formulation of physical
laws in science, and considering the "experiential" side of these
representational practices,we must, then, at the very least least attempt
to distinguish between our law of gravity as:
Third: a coded (linguistic or mathematical) statement of the habitual
physical relationships that obtain between separate bodies with mass which
is generally accepted by the scientific community as the best explanation
of the facts
Second: the "brute fact" of gravitational attraction (constituting I guess,
the " real reason" that the law actually needs to be formulated in the way
it is) i.e. that this experienced/ observed "falling down" represents a
habitual tendency of material objects suddenly released from some point
above the surface of the earth to gravitate towards its center until they
are stopped by the surface
First: the "experiential fact" of gravity, perceived in what we also could
call embodied, common sense terms (i.e. that seen from a
right-way-up-human-observer-in-a-body's point of view, things including
oneself in any part of the world, tend to fall "down" if not mechanically
or otherwise driven, or supported in some way from above or below).
Here Mark's point about the paper clip and the desk is of course by no
means out of place, it's just that by and large we do in practice (there's
that word again) tend to take the general effects of gravitational
attraction to be unidirectional (ie. the body with the smaller mass as
being attracted towards that with the larger), while in fact this
attraction is bi-directional, or perhaps put in a better way, mutual.
This tendency to a unidirectional view of things actually supports very
well your discussion of global map-drawing practices and our tendency in
the cosy old-world "northern" hemisphere to consider ourselves as walking
feet down, while Australians must just be doing something else altogether -
hanging upside down by their feet like so many bungee-jumpers - when in
fact we are all, wherever we are in the world, just pointing towards the
center from our head and down to our toes like cloves stuck into the skin
of an orange at Christmas.
Remember of course, that any tendency to differ, however "congenital" or
gravitationally induced it may be, is from my point of view at least, by no
means a negative quality... :)
All best, and thanks for a stimulating response to my joke...
Patrick
PS
In passing and apropos of maps, I vaguely recall reading once that Peirce
had worked at one time on developing a new type of projection for the map
of the world. Do you (or anyone else) happen to know just how that
alternative representation was thought to be?
P.
_______________________________________________________________
Patrick J. Coppock tel. +47 73 59 08 71 (office)
The Norwegian University of tel. +47 73 59 88 70 (lab)
Technology and Science tel. +47 72 55 50 91 (home)
Dept. of Applied Linguistics fax: +47 73 59 81 50 (Norway)
N-7055 Dragvoll, Norway : +39 51 33 29 39 (Italy)
e-mail:
patcop[…]alfa.itea.ntnu.no (Norway)
patcop[…]bo.nettuno.it (Italy)
WWW http://www.hf.ntnu.no/anv/wwwpages/PJCHome2.html
_______________________________________________________________
"What is seductive about the causal approach is that it leads
one to say: "Of course, that's how it must be". While one
ought to think: In this, and in many other ways it may have
occurred." L. Wittgenstein, 2.7.1940
_______________________________________________________________
------------------------------
Date: Thu, 12 Mar 1998 11:21:11 +0100 (MET)
From: Howard Callaway
To: Multiple recipients of list
Subject: Re: Logic Naturalized : Truth
Message-ID:
The recent exchange between Tom Burke and Joe Ransdell, and
Cathy's question, have helped stimulate the following
thoughts on the syntax/semantics distinction. I should
perhaps preface the following by saying, for the sake of
those more recent folks on the Peirce-l, that I've always
been fairly favorable toward the Tarskian conception of
truth. But on the other hand, this does have its limits,
since I suppose that there are undiscovered truths which
existing languages may be unable to formulate, and the
Tarskian conception of truth focuses on providing truth
definitions for specified languages.
The deeper question, of course, concerns the compatibility
of the semantic conception of truth with Peirce's accounts
of meaning, reference, and interpretation. But I do not see
that we are forced to construe Tarskian semantics as anti-
triadic. On the contrary, I think that in Tarskian seman-
tics, one is concerned with the reference of signs to things
in relation to an interpretation or interpretations. For
instance, one could say that an argument is valid iff the
conclusion is true (and thus relevant terms denote or refer
to relevant objects/things) on every consistent or uniform
interpretation which renders the premises true. It seems to
me that Tarskian semantics makes essential use of a concep-
tion of interpretation.
Filling in the specifics of this conception of interpreta-
tion is what may make the difference. Davidson's work helped
to clarify the point that Tarski's theory of truth depends
upon an implicit notion of translation or synonymy. "In Tar-
ski's work," writes Davidson, "T-sentences are taken to be
true because the right branch of the biconditional is
assumed to be a translation of the sentence truth-conditions
for which are being given." That is, "assuming translation,
Tarski was able to define truth" (Davidson, 1973, "Radical
Interpretation," _Dialectica_ 27, pp. 313-28. Reprinted in
Davidson (1984) _Essays on Truth and Interpretation_, see p.
134). A notion of translation is assumed by Tarski in the
form of a relation between sentences of the object language
and sentences of the semantic metalanguage. The plausibility
of the truth paradigms, and typical T-sentences, for
instance,
"Snow is white" is true-in-English iff snow is white.
starts from the implicit assumption that the sentence on the
right, used to express truth-conditions, is semantically
indistinguishable (i.e. indistinguishable as concerns mean-
ing or interpretation) from the sentence mentioned, the sen-
tence for which truth-conditions are being given. Thus, if
we stipulate, contrary to this assumption, that the meaning
(or interpretation) and reference of expressions of the
object language are not the same as those of the correspond-
ing expressions of the metalanguage, then we no longer have
reason to accept the T-sentences as paradigms for "true." If
we employ the semantic conception of truth, then, we pre-
suppose the cogency of sameness of meaning (or interpre-
tation) and of the fundamental semantic notion of satisfac-
tion. Beyond that, once we are in a position to formulate T-
sentences, it seems that any theory of truth must take them
into consideration in some way or other.
Actually, I think there is nothing very startling in Tarki's
implicit assumption of a synonymy relation. (What is perhaps
startling is that Davidson should have explicitly emphasized
this point, given Quine's skepticism concerning meanings.)
But this kind of point is implicit in the tradition since
Aristotle. We can see the point most clearly, I think, by
considering that valid forms of inference (identified by
reference to syntax and orthography or vocabulary) can lead
from true premises to false conclusions, if the interpre-
tations of the terms are not uniform throughout the argu-
ment. We have to avoid fallacies connected with ambiguity.
This is one point where interpretation comes into the
picture.
Since Frege, this has tended to take the form of insisting
on a "logically perfect language," in which ambiguities are
already excluded. But if language must advance with the
advance of inquiry, and we are sometimes left unsure of the
results of inquiry, we will also sometimes be unsure of
whether we are dealing with a "logically perfect language."
The concept is much less suited to a logic of research or
inquiry, as contrasted to a logic of exposition of the
accepted results of inquiry.
But our ability to detect ambiguity ultimately depends on
recognizing truths, or supposed truths, which distinguish
"terms" (or "concepts") in ways not depending on sameness or
difference of words or expressions. Whether we see recogni-
tion of logical validity as depending on prior exemplifica-
tions (the continuity of logical forms and subject-matter,
as in Dewey) or on a Peirce-like "phenomenology," of con-
cepts thus comes to depend on the coherence of a phenomeno-
logy of concepts which makes no substantial use of the
results of specific inquiries. Its worth remarking, in this
connection, that Peirce does not maintain a full metaphysi-
cal neutrality. Instead the phenomenological categories, for
instance, are preliminary to his metaphysical categories.
Where advances in logic may depend on specific results of
specialized inquiries, then it seems that the phenomeno-
logical neutrality --accounting for (formal or quasi-formal)
validity without recourse to claims of soundness or "better
and worse" in practice-- must be surrendered. A purely
phenomenological grounding of logic, independent of any
applications or exemplification, would seem to be anti-prag-
matic. This point seems to bring us back to needed refine-
ments of anti-psychologism. In considering the meaning of
logical claims, we have to look at what differences they
make to possible experience; and their truth or validity
cannot be totally divorced from testing in experience.
It seems clear, in any case, that Peirce cannot avoid a
syntax/semantics distinction in some form, since this is
present wherever we distinguish distinct meanings or inter-
pretations of the same word or expression.
Howard
H.G. Callaway
Seminar for Philosophy
University of Mainz
------------------------------
Date: Thu, 12 Mar 1998 12:15:21 -0500
From: Hugo Fjelsted Alroe
To: peirce-l[…]ttacs6.ttu.edu
Subject: Re: Logic Naturalized : Truth
Message-ID: <3.0.2.32.19980312121521.00732a0c[…]vip.cybercity.dk>
>From my naive viewpoint, the relation between the Tarskian syntax/semantics
distinction and Peirce's logic or semeiotics seems quite straight forward.
Perhaps I have missed some important point, and I hope someone can tell me
where the following goes astray.
The paradoxes of logic, both those now called syntactic, and those now
called semantic paradoxes, were resolved by some use of the concepts of
reference or representation. The socalled syntactic paradoxes have been
resolved by putting limits on reference, whether in form of Russels theory
of logical types, or in form of Goedels limit theorem on provability. And
the socalled semantic paradoxes have been resolved by making some explicit
system of reference, like Tarski's concepts of object language and meta
language. As you may sense, I do not see the distinction between syntactic
and semantic paradoxes as very useful, basically the paradoxes and the
resolutions are of the same kind. And the resolutions are also moves in the
same direction as Peirce's move in logic; Peirce's semeiotics is based on
reference or representation, this is what a sign is about.
Now, what does this mean for the relation between the syntax/semantics
distinction and Peirce's logic? Or, in other words, how have the logical
paradoxes been, or how should they be, resolved within the Peircean logic?
I suppose Peirce or somebody else have long past explicated this, and I
suppose it goes something like this: In a logic with no explicit way of
handling reference, paradoxes will arise. The seeming paradox in "This
sentence is false" can only be resolved by explicating the signs of
reference at play. What is the reference of "this sentence"? This is
equivalent to asking: What is this image a mirror of?, pointing to one of
two mirrors mirroring each other. Such messy infinities are necessarily
implied by any open system of reference or representation. So the Peircean
answer must be, these paradoxes are only paradoxes if the referential
nature of reference is ignored, that is, if signs are taken to be objects.
The very form of this answer shows how a semeiotic logic has already
stepped beyond the ground where these paradoxes arise.
The distinction between syntax and semantics, between provability and
truth, is a distinction between syntactical truth and semantic truth, that
is, between two kinds of truth. How does this relate to semeiotics?
Following from the above, the semantic truth, the truth of reference, must
be exactly that, a referential truth. The truth of the sentence "This
orange is green" is unavoidably connected with the specific reference of
"this orange". On the other hand the syntactic truth is the not-referential
truth, it is the truth which does not depend on any frame of reference.
Is there any place for such a syntactic truth in a semeiotic logic? I would
say: not really. A syntactic truth is a truth where we do not question the
frame of reference, or the context, to use another often used term.
Pragmatically, there are of course at any point in inquiry some frame of
reference which is not questioned. But saying that syntactic truth has a
not only pragmatic role to play in semeiotics, is to say that there are
frames of reference which could never be questioned, that there is an
absolute stance, in other words. I would say there is no absolute stance,
Peirce might say otherwise, but I think the question is pivotal in
explicating the relation between the syntax/semantics distinction and
Peirce's semeiotics.
Prepared to be wrong
Hugo
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Hugo Fjelsted Alroe alroe[…]email.dk alroe[…]vip.cybercity.dk
------------------------------
Date: Thu, 12 Mar 1998 13:07:15 +0100 (MET)
From: Howard Callaway
To: peirce-l[…]ttacs6.ttu.edu
Subject: Dyadic vs. Triadic?
Message-ID:
The following short quotation from Carl Hausman's _Charles
S. Peirce's Evolutionary Philosophy_ may help clarify what
is involved in rejecting any "dyadic" conception of signs:
...what needs emphasizing is that signs are not simply
dyadic relations in which something called a sign
stands for an object. For a sign to be meaningful it
must function in a triadic relation in which sign and
object interact with interpretation. This implies that
signs function in ongoing processes of interpretation;
however, their semeiotic meaning is never exhausted by
any finite context of interpretation (p. 9).
What I emphasized in my prior posting was the way in which
the sign-object relation depends on, or is provided in
relation to, an interpretation in Tarskian semantics. Of
course this is not quite the same as saying that "sign and
object interact with interpretation." Saying this kind of
thing emphasizes, I think, the process aspect of logic, or
the point that Peirce's logic is a logic of research or
inquiry, in contrast to a logic of exposition of established
results of inquiry. The same can be said for Dewey's logic.
If the semeiotic meaning is "never exhausted by any finite
context of interpretation," then this suggests a fallibi-
listic openness regarding any interpretation which we pre-
sently hold or work with. But on the other hand, it seems
obvious that we are never going to be in a position to
employ or use every eventual or potential interpretation
which may arise in the future. We naturally make use of
those interpretations presently available, which seem most
securely grounded.
So long as we are concerned with any particular interpreta-
tion actually available to us, then, the (future) interac-
tion of sign and object with interpretation is to the point
only as a matter of leaving ourselves open to future
developments. In fact, if we view the relation of sign and
object to interpretation, in Tarskian semantics, as the
result of past "interactions," then no conflict between
Peirce and Tarskian semantics seems to arise. So, while
Tarski's conception of truth only allows for definition of
truth for specified languages, this does not seem to forbid
the prospect of applying more or less the same approach to
new (or revised) languages which arise in connection with
further inquiry.
Likewise, Tarskian semantics is tied to set theory. But if
we observe how the needed set-theoretical configurations
evolve as a consequence of re-interpretation, as required by
the advance of inquiry, then it seems that contrasting set-
theoretical configurations of objects, sets, and subsets,
etc. might be viewed as "growing" the later from the ear-
lier, in somewhat the way that points emerge in a Peircean
line as a result of mathematical operations.
However this may be, it seems more important to emphasize
that the "interaction" of which Hausman speaks can be
understood as the process by which one Tarskian interpre-
tation of a term is related to another. So, for example, if
we provided a Tarskian semantics for Ptolemaic astronomy,
then certain objects, say the sun, will get counted as
members of the set of satellites of the earth. But moving on
to Copernican astronomy, the sun is no longer counted as a
member of the set of satellites of the earth. This differ-
ence reflects differences in the interpretations provided to
the relevant terms. It is in moving from one interpretation
to another that the sign and object might be said to "inter-
act" with the interpretation.
I hope this will be helpful. It seems to me that the basic
problem concerns the interest among Peirce scholars for this
kind of comparison. I think of myself as following Putnam's
lead here in comparing Peircean conceptions with those cur-
rent in the wider world. From this perspective Peirce's
emphasis on potentiality, development, and inquiry seems
more important than does the contrast of two vs. three.
But I believe that genuine improvements always depend on
clarity about where we presently stand, and that is what
Tarskian semantics is all about: it is a way of being seman-
tically explicit (as regards interpretation) in relation to
the currently accepted results of inquiry.
Howard
H.G. Callaway
Seminar for Philosophy
University of Mainz
------------------------------
Date: Thu, 12 Mar 1998 23:24:55 +1100 (EDT)
From: Cathy Legg
To: peirce-l[…]ttacs6.ttu.edu
Subject: RE: Logic Naturalized : Truth
Message-ID:
On Tue, 10 Mar 1998, Tom Burke wrote:
> >No, Tom, Goedel's theorem is a purely syntactic result. (This is
> >where many popular expositions of Goedel's Theorem are confusing, as they
> >tell a semantic story to give you the idea quickly and easily).
> >
> >That is to say that Goedel's theorem does not necessarily describe the
> >incompleteness of arithmetic. Sure that is one interpretation of it
> >(which has been quite useful!), but it could also describe the
> >"incompleteness" of other recursively structured languages, if we could
> >interpret accordingly.
>
> I am no expert on the details and interpretation of Goedel's incompleteness
> theorem, but I don't think it is merely a syntactic result. The proof
> itself focuses on the syntax for a language rich enough to handle
> arithmetic, but I was careful to refer to "interesting (contentful)" formal
> systems, not just to arithmetic. So we agree that it is not just a result
> concerning mathematics, but applies to all sorts of recursively structured
> formal systems.
On the whole I agree with Joe and Anne that the syntax/semantics
distinction is not sharp enough to be useful in talking about
natural language. So, for instance, the statement, "All bachelors are
unmarried" is a tautologously true, but is this due to "syntax" or to
"semantics"? Well this depends how the statement is formalised...
I think that the distinction *can* be defined clearly in certain formalised
systems of logic, and there "syntax" refers to the explicitly defined
rules (and maybe the axioms too, I'm not sure) of that logical system,
while "semantics" refers to the *interpretation* given to the logical
system, that is the way its variables (and predicates) are mapped onto
"things in the world". The semantics is left open by the syntax - that
is, other interpretations are possible.
If we clarify the two terms in this way, then Goedel's result *is* purely
syntactic, and I would refer Tom to chapter 3 of Mendelson, _Introduction
to Mathematical Logic_, (New York : Van Nostrand, 1979.)
> To say that it is purely a syntactic result is something else altogether.
Not according to the definitions above. What definitions do you favour, Tom?
> Truth in Tarski's if not Goedel's sense is a semantic notion, and we can
> talk about truth and consequence in a model or in "every" model (i.e., in a
> semantic sense) independent of syntactic proof. On one hand you have
> consequence relations in a semantic sense,
Do you mean "necessary connections"? I was going to say that I think
necessary vs. contingent connections is the really useful distinction in
this vicinity, but it carves up logical space rather differently than
"syntactic" vs. "semantic".
> and on the other hand, you have
> deducibility relations relative to a given proof system. Goedel's
> completeness theorems were results concerning the correspondence between
> these two kinds of relations; and sure enough, they line up in simpler
> cases (truth-functional languages; first-order predicate calculi; etc.) but
> they don't once your semantics is interesting enough [...]
Why not "once your syntax is interesting enough"...?
Cheers,
Cathy.
{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{
Cathy Legg,
Philosophy Programme,
RSSS, ANU, ACT, AUS.,
0200.
Why is the alphabet in that order? Is it because of that song?
http://coombs.anu.edu.au/Depts/RSSS/Philosophy/People/Cathy/Cathy.html
}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}
------------------------------
Date: Thu, 12 Mar 1998 23:33:46 +1100 (EDT)
From: Cathy Legg
To: peirce-l[…]ttacs6.ttu.edu
Subject: Re: Logic Naturalized?
Message-ID:
On Tue, 10 Mar 1998, Tom Burke wrote:
> At 7:09 AM -0500 3/6/98, Cathy Legg wrote:
> >
> >I'd say we get "extensions" in logic, but we don't get "revisions", (if by
> >revisions is meant changing one's mind about what is valid). In this it
> >is like mathematics. Or maybe this is assimilating logic too much to
> >deductive logic?
>
> Sorry to keep harping on all of this, but it seems important to me that we
> should recognize how it is that logic does get "revised", not just
> extended. For Aristotle, e.g., logic and ontology were inextricably bound
> up with one another; whereas we have now revised this conception of what
> logic is all about. Logical positivists also had a view of logic and its
> relationship to metaphysics and epistemology which have been revised in the
> meantime. Logicians do a bunch of stuff that gets interpreted and applied
> in various ways; and these interpretations are, as history amply shows,
> fallible. We no doubt still don't quite have it right.
Yes but I was careful to explain what I meant by "revise" as "changing
one's mind about what's a valid argument." Can Tom or anyone else give me an
example of where that has happened in the history of logic?
> Howard is talking about revision in a different sense, I think, which might
> be better termed "modification" or something like that. E.g., there are
> lots of different modal logics, all of which are variations on a theme, but
> no one of which is *the* standard of validity, or *the one true logic*.
> Mathematical logicians just don't worry about that kind of thing anymore,
> but explore different extensions/modifications of the logical systems they
> are so far acquainted with.
I do agree that the development of formal logic (which was made possible
through logic getting detached from rhetoric, perhaps?) has now complicated
matters enormously, making validity more formalisation-relative...
I think talking about some examples here would make our thinking more
pragmatical.
Cheers,
Cathy.
{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{
Cathy Legg,
Philosophy Programme,
RSSS, ANU, ACT, AUS.,
0200.
Why is the alphabet in that order? Is it because of that song?
http://coombs.anu.edu.au/Depts/RSSS/Philosophy/People/Cathy/Cathy.html
}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}
------------------------------
Date: Thu, 12 Mar 1998 13:36:12 +0100 (MET)
From: Howard Callaway
To: Multiple recipients of list
Subject: Re: Logic Naturalized : Truth
Message-ID:
On Thu, 12 Mar 1998, Hugo Fjelsted Alroe wrote:
> The distinction between syntax and semantics, between provability and
> truth, is a distinction between syntactical truth and semantic truth, that
> is, between two kinds of truth. How does this relate to semeiotics?
Hugo,
There are several interesting points in your posting which I might like
to address. However, time limits me to trying to say something about
the paragraph I quote here. Basically, your opening puzzles me, since I
don't think anyone would want to take up a distinction between "two
kinds of truth" on the basis of the syntax/semantics distinction (unless
this be the pure a priori formalist). So, in order to answer your question
above, I'd first want to know the what and why of your notion of "two
kinds of truth."
> Following from the above, the semantic truth, the truth of reference, must
> be exactly that, a referential truth. The truth of the sentence "This
> orange is green" is unavoidably connected with the specific reference of
> "this orange". On the other hand the syntactic truth is the not-referential
> truth, it is the truth which does not depend on any frame of reference.
In talking about "syntactic truth" I assume that you mean something like
truths that can be demonstrated on the basis of rules applied in
connection with syntactic criteria of sameness and difference of
expressions. For example, we might make use of a system of logical rules
to prove a theorem of logic, say Peirce's law. But I'm not tempted to
look at this in purely formalistic terms. Instead, I think of the rule
and their use as presupposing or assuming an interpretation of the
signs or symbols involved. Formalistically minded logicians may resist
this, but that point is nether here nor there. If we apply logical rules
to generate a proof of a logical truth, then I think this assumes that
the symbols involved are to be interpreted uniformly. In any actual
application, where some particular vocabulary is operated on (and
we are not dealing with stand-ins for actual, referential vocabulary),
then the uniformity of the interpretation of those signs or symbols
is, of course, open to question.
> Is there any place for such a syntactic truth in a semeiotic logic? I would
> say: not really. A syntactic truth is a truth where we do not question the
> frame of reference, or the context, to use another often used term.
> Pragmatically, there are of course at any point in inquiry some frame of
> reference which is not questioned. But saying that syntactic truth has a
> not only pragmatic role to play in semeiotics, is to say that there are
> frames of reference which could never be questioned, that there is an
> absolute stance, in other words. I would say there is no absolute stance,
> Peirce might say otherwise, but I think the question is pivotal in
> explicating the relation between the syntax/semantics distinction and
> Peirce's semeiotics.
>
I agree with you that there is no "absolute" stance. Although there is
always some frame of reference which we don't in fact question at the
moment, this is far from saying that there is a frame of reference which
"could never be questioned."
So, perhaps I agree with you in the end. Syntactic rule of inference
can certainly be employed "pragmatically," as you say. I think this
should mean that they can be employed so long as they do not become
problematic, in guiding us from truths to further truths. Again, it
means to me that they can be employed only with needed cautions concerning
the vagaries of reference and interpretation.
Cheers!
Howard
H.G. Callaway
Seminar for Philosophy
University of Mainz
------------------------------